Most shrimp is frozen soon after being caught, so though it seems counterintuitive, the freshest-tasting shrimp is the kind you buy in the freezer aisle rather than the thawed stuff at the supermarket fish counter. (Learn more about how to choose the best shrimp). Shrimp is highly perishable, and you don’t really know how long the thawed stuff has been thawed.
If you buy frozen shrimp, you can thaw it yourself just before you need it. Let it thaw overnight in the fridge, or for faster thawing, take the shrimp out of its package, put it in a bowl of cold water, and let a trickle of cold water run into the bowl while excess water goes down the drain. The shrimp should be ready to cook in about 15 minutes.